Question: Simplify the following expression: $ z = \dfrac{9y - 3}{-3y - 3} - 5 $
Answer: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-3y - 3}{-3y - 3}$ $ \dfrac{-5}{1} \times \dfrac{-3y - 3}{-3y - 3} = \dfrac{15y + 15}{-3y - 3} $ Therefore $ z = \dfrac{9y - 3}{-3y - 3} + \dfrac{15y + 15}{-3y - 3} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{9y - 3 + 15y + 15}{-3y - 3} $ $z = \dfrac{24y + 12}{-3y - 3}$ Simplify the expression by dividing the numerator and denominator by -3: $z = \dfrac{-8y - 4}{y + 1}$